In the diagram, the area of triangle $ABC$ is 27 square units. What is the area of triangle $BCD$?

[asy]

draw((0,0)--(32,0)--(9,15)--(0,0));

dot((0,0));
label("$A$",(0,0),SW);
label("6",(3,0),S);
dot((6,0));
label("$C$",(6,0),S);
label("26",(19,0),S);
dot((32,0));
label("$D$",(32,0),SE);
dot((9,15));
label("$B$",(9,15),N);

draw((6,0)--(9,15));

[/asy]
Explanation: Let $h$ be the distance from $B$ to side $AD$.  The area of $ABC$ is 27, so $\frac{1}{2}\cdot6\cdot h = 27$, which implies $h=9$.  The area of $BCD$ is $\frac{1}{2}\cdot26\cdot9=\boxed{117}$ square units.